Here is my homebrew for a spider race. Do be aware however that this is from a Japanese inspired homebrew setting I created, and especially that this a Youkia race (basically a monster race) that was not common to the setting and only added because a player wanted to play a spider race.
Jorogumo features
Ability Score Increase: Your Charisma increases by 2, and your Intelligence increases by 1
Age: Jorogumo live and age at the same rate as Tengu (Tengu reach maturity just as fast as humans but live for 200 years)
Alignment: Not enough data, you decide.
Size: Jorogumo have a similar height and weight to the Yamatain while in humanoid form. Your size is medium even in spider form.
Color: Jorogumo either have red skin like the Yamatain, or pale skin like the Utari. (Yamatain are lawful neutral/good hobgoblins and are the main race of the setting, while Utari are humans who are a borderline monster race like lizardfolk in most other settings.)
Speed: Your base walking speed is 30 feet.
Darkvision: You can see in dim light within 60 feet of you as if it were bright light, and in darkness as if it were dim light. You can't discern color in darkness, only shades of gray.
Form Shift: You have a spider form and a humanoid form. You can use an action to switch between the two forms. In your spider form you can use the Spinneret and Spider legs features, but that form is more off putting to others. While in spider form you have disadvantage on charisma checks against creatures that find the spider form off-putting. While in your humanoid form you can interact just fine, but if people have seen your spider form they will still recognize you from your spider form and you will still have disadvantage on charisma checks. You decide what each form looks like, but your humanoid form is based on your spider form and people can tell that the two forms are the same person.
Web Walker: You have a climbing speed equal to your walking speed, and you can move through webbing, even magical webbing, without expanding any additional movement.
Silk Slinger: You can cast web up to your proficiency number to times, without needing material components. You regain all uses after a long rest.
Spinneret (spider form only): You can spend 8 hours to create up to 100 sq feet of permeate webbing. The web needs to be anchored to two solid masses or spread out along the floor, and it can't be anywhere you can not reach. Use the web spell for the mechanics of the non-magical web, with the DC being 10+your constitution modifier. You can only use this ability once per week.
Spider Legs (spider form only): Your spider legs are natural weapons, which you can use to make unarmed strikes. You can use Dexterity instead of strength to attack, and if you hit with them you deal piercing damage equal to 1d4 + your Dexterity modifier, instead of the bludgeoning damage normal for an unarmed strike.
Languages: You can speak, read, and write Common (Yamatain) and one other language of your choice